The equilibrium expression has to be expressed for given reaction.
Equilibrium expression: The equilibrium expression is equal to the concentration of each product raised to its coefficient in a balanced chemical equation and multiplied together, divides by the concentrate ions of the product of reactants to the power of their coefficient.
Equilibrium constant: Concentration of the products to the respective molar concentration of reactants it is called equilibrium constant. If the K value is less than one the reaction will move to the left side and the K values is higher (or) greater than one the reaction will move to the right side of reaction.
Homogeneous equilibrium: A homogeneous equilibrium involved has a everything present in the same phase and same conditions, for example reactions where everything is a gas, or everything is present in the same solution.
Heterogeneous equilibrium: This equilibrium reaction does not depend on the amounts of pure solid and liquid present, in other words heterogeneous equilibrium, substances are in different phases.
and : This equilibrium constants of gaseous mixtures, these difference between the two constants is that is defined by molar concentrations, whereas is defined by the partial pressures of the gasses inside a closed system.